Okay i got 8 and 5 for the second which check out but 0 and -2 don't check with the original first problem

Actually, you're right. The first problem doesn't have any solutions. You have to check, once you get possible answers, whether they really solve the equation. If the problem had been instead then those two solutions would be correct.

From here it should be clear that, as you have already discovered, there are no solutions, because no matter the value of x, |2x| will always be greater than it, and so |2x|-x will always be greater than or equal to zero, and thus can never equal -2.

Be sure to see that the method that icemanfan showed you still works; you just have to be careful about your signs:

Considering the two cases separately:

, but this contradicts our requirement that so it is not a solution.

, but this contradicts our requirement that so it is also not a solution.

These are the only two possibilities (from the trichotomy law), so the original equation has no solutions.

It is, however, always a good idea to check your values in the original equation, because unless you are very careful in performing operations you can easily end up with extraneous (and sometimes missing) solutions.

From here it should be clear that, as you have already discovered, there are no solutions, because no matter the value of x, |2x| will always be greater than it, and so |2x|-x will always be greater than or equal to zero, and thus can never equal -2.